⚡ Sorting Algorithm Complexity 📖

⚡ Sorting Algorithm Complexity

Legend

• Ω (Omega) → Best case
• Θ (Theta) → Average case
• O (Big O) → Worst case
• Stable? ✅ Yes / ❌ No

#	Algorithm	⏱️ Best	⚖️ Average	🔻 Worst	💾 Space	⚙️ Stability
1️⃣	⚡ Quick Sort	Ω(n log n)	Θ(n log n)	O(n²)	O(log n)	❌ No
2️⃣	🧩 Merge Sort	Ω(n log n)	Θ(n log n)	O(n log n)	O(n)	✅ Yes
3️⃣	🚀 Timsort	Ω(n)	Θ(n log n)	O(n log n)	O(n)	✅ Yes
4️⃣	⛰️ Heap Sort	Ω(n log n)	Θ(n log n)	O(n log n)	O(1)	❌ No
5️⃣	💧 Bubble Sort	Ω(n)	Θ(n²)	O(n²)	O(1)	✅ Yes
6️⃣	✍️ Insertion Sort	Ω(n)	Θ(n²)	O(n²)	O(1)	✅ Yes
7️⃣	🪞 Selection Sort	Ω(n²)	Θ(n²)	O(n²)	O(1)	❌ No
8️⃣	🌲 Tree Sort	Ω(n log n)	Θ(n log n)	O(n²)	O(n)	✅ Yes
9️⃣	🐚 Shell Sort	Ω(n log n)	Θ(n (log n)²)	O(n (log n)²)	O(1)	❌ No
🔟	🪣 Bucket Sort	Ω(n + k)	Θ(n + k)	O(n²)	O(n)	✅ Yes
1️⃣1️⃣	🔢 Radix Sort	Ω(n k)	Θ(n k)	O(n k)	O(n + k)	✅ Yes
1️⃣2️⃣	🧮 Counting Sort	Ω(n + k)	Θ(n + k)	O(n + k)	O(k)	✅ Yes
1️⃣3️⃣	🧊 Cube Sort	Ω(n)	Θ(n log n)	O(n log n)	O(n)	✅ Yes

---

Related Posts

• 🧱 Data Structures & Big O Complexity — the Big O/Big Omega/Big Theta notation used throughout this comparison
• 🔎 Searching Algorithm Complexity — Binary Search and other sorted-data-dependent searches this sorting step enables